Multiplayer input lag

[Gugernoot215]

The last time I've played multiplayer with a bad internet connection, it was horrible.
Why is input lag dictated by your connection rather than you local machine?
Wouldn't it make sense to have the in game machine run locally then your information is broadcasted rather than your inputs. Interaction with physics objects would also happen locally although problems would arise when out of sync players are interacting with the same objects.
Giants already have a system of disabling physics objects when they are out of range so it would make sense that when a player is in range interaction is then enabled for them locally.

I've played Mudrunner with poor internet and it works great because the game is run locally so you can drive just as well as you can in singleplayer as input lag is the same. Desync is dealt with by disabling interaction with people you aren't synchronised with. Logs have to transferred to other players for them to interact with so I don't think that system would work in farming simulator for objects when two players can interact with an object.

What do you think?